In this extended abstract, we extend recent results of Assaf and McNamara, the skew Pieri rule and the skew Murnaghan-Nakayama rule, to a more general identity, which gives an elegant expansion ofâ€¦ (More)

Following the work of Okounkov-Pandharipande [OP1, OP2] and Diaconescu [D], we study the equivariant quantum cohomology QHâˆ— (Câˆ—)2(Hilbn) of the Hilbert scheme and the relative Donaldson-Thomas theoryâ€¦ (More)

We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are inâ€¦ (More)

We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-LÃªZeilberger. The proofs are combinatorial and new evenâ€¦ (More)

Abstract. Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The first proof isâ€¦ (More)

In this paper we analyze Oâ€™Haraâ€™s partition bijection. We present three type of results. First, we see that Oâ€™Haraâ€™s bijection can be viewed geometrically as a certain scissor congruence type result.â€¦ (More)

Sylvesterâ€™s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a Î²-extensionâ€¦ (More)

We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such numbers when p is a prime and q its power.